I just figure out what they're into and buy a relevant item as a gift.

I remember when my nephew wanted a Lego Duplo combine harvester for his birthday and my mother scoured high and low for one and was ready to call it quits when I was like "no, we will get this kid what he wants" - so I had her give me the money, scored one on ebay and got him his combine harvester.

As a kid, I rarely got what I asked for, so that kind of inspired me to not let him down.